plumiInvariant points and lines: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 3.5 Invariant points and lines, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 7 questions on Invariant points and lines, as a list
- June 2023, Core Pure, Q6 (9 marks): J N J N The matrices M and N are 0 1 OO and 2 0 KK KK OO respectively. 6 1 0 0 1 L P L P (a) In this question you must show detailed reasoning. Determine whethe
- June 2023, AS Core Pure, Q9 (6 marks): J N k 1 1 + - KK OO, where k is a 9 A transformation T of the plane is represented by the matrix M = 1 k constant. L P Show that, for all values of k, T has no
- June 2022, AS Core Pure, Q8 (12 marks): J N cos 2 cos sin - i i i KK OO. 8 A transformation T of the plane has matrix M, where M = sin 2 sin cos + i i i L P (a) Show that T leaves areas unchanged for
- November 2021, Core Pure, Q6 (4 marks): J N is an invariant line of the transformation with matrix 1 2 KK OO, determine the 6 Given that y mx = 2 2 - L P possible values of m. [4]
- November 2020, Core Pure, Q9 (8 marks): J N 1 2 - KK OO, where m is a 9 A linear transformation of the plane is represented by the matrix M = 3 m constant. L P (a) Find the set of values of m for whic
- June 2019, AS Core Pure, Q6 (11 marks): J N k m KK OO, and m 6 A linear transformation T of the x-y plane has an associated matrix M, where M = 1 k - m and k are real constants. L P (a) You are given
- June 2018, AS Core Pure, Q6 (4 marks): Find the invariant line of the transformation of the x-y plane represented by the matrix 2 c 0 m. 6 [4] 4 1 -
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